Results and Analysis

I compare the performance of EELA with that of OLTC [63], EELA-min, and EELA-max for UWSNs. For each simulation, the number of deployed sensor nodes is varied between 10 to 50. Each simulation runs for 5000 times to obtain the average results.

1) Localization Coverage: In Fig. 4.3, the average localization coverage in function of the number of sensor nodes is presented.

I observe that the average localization coverage of both EELA and OLTC are between that of EELA-Max and EELA-Min, as expected. 3DUL-Max [64] has the same performance with that of EELA-Max while 3DUL-Min [64] performs better than EELA. The proposed EELA scheme outperforms the reference OLTC scheme of [63].

For all schemes, an increased number of sensor nodes results in a better localization coverage. This is because the increase of the number of sensor nodes entails a higher spatial density, hence more sensor nodes may be localized by anchor nodes with a given power.

Compared to OLTC, the localization coverage achieved by EELA is2.0 %higher on average. This is because in OLTC scheme, sensor nodes always send request with the maximum transmission power, which leads to a higher rate of packet collision.

Thus, anchor nodes will receive fewer ‘Request’ messages. However, anchor nodes use the optimal transmission powerP_j < P_maxto reply, so that some sensor nodes may not receive the required number of anchor nodes, hence decreasing coverage.

By contrast, in EELA, sensor nodes request with the optimal transmission power P_j < P_maxinstead of using the maximum transmission power, so that the required number of anchor nodes may be reached with minimum energy consumption. On the other hand, anchor nodes also utilize the optimal transmission power to reply.

Both the optimal transmission power for anchor node and sensor node are selected to reach Stackelberg Nash Equilibrium in section 4.6.1.4. Hence, both anchor nodes and sensor nodes cannot improve their individual profit by single-sidedly changing their transmission power. Therefore, EELA can reduce the rate of packet collision, and achieve a higher coverage.

Compared to EELA-Min, the localization coverage achieved in EELA is about54 % higher on average, because sensor nodes always use the minimum transmission power to send ‘Request’ messages while anchor nodes also use the minimum trans-mission power to reply, hence each sensor node receives the fewest beacon location

10 20 30 40 50 50

60 70 80 90 100

Number of Sensor Nodes

LocalizedNodes(%)

EELA OLTC 3DUL-Min

3DUL-Max EELA-Min EELA-Max

Figure 4.3: Localization coverage.

messages to localize itself. Next, the localization coverage achieved in EELA-Max is about9 %(on average) higher than that in EELA. For EELA-Max, although the

‘Request’ messages from sensor nodes have higher probability to have collisions, anchor nodes always use the maximum transmission power to send ‘Reply’ mes-sages without considering received requests. Therefore, sensor nodes can always receive more beacon locations than those of other schemes. That is the reason why EELA-Max always has the highest coverage However, the use of higher transmission power leads to higher energy consumption, as shown next. In 3DUL-Max and 3DUL-Min, the localized sensor nodes can be used as new anchor nodes to help other sensor nodes to get their locations, which leads to higher localization coverage.

However, the energy consumption for sensor nodes is very high and the localization error as well as delay are accumulated due to the iterative localization design in 3DUL.

2) Average Energy Consumption Per Sensor Node: The average energy consumption results for sensor nodes are given in Fig. 4.4.

I observe that the performance of the proposed EELA scheme is between that of EELA-Min and EELA-Max, while OLTC has the same consumption as EELA-Max since all sensor nodes transmit with maximum power. 3DUL-Max consumes the highest energy for sensor nodes among all the schemes because after sensor nodes of 3DUL-Max get their locations, sensor nodes can transform to change to anchor nodes to help other sensor nodes to get their locations in order to achieve high

10 20 30 40 50 0

200 400 600 800 1,000 1,200

Number of Sensor Nodes

Avg.EnergyCostperSN(J)

EELA OLTC 3DUL-Min

3DUL-Max EELA-Min EELA-Max

Figure 4.4: Average energy consumption per Sensor Node (SN).

coverage. In a similar way, the energy consumption of 3DUL-Min is higher than that of EELA-Min. In OLTC, EELA-Min, EELA-Max, 3DUL-Min and 3DUL-Max, the average energy consumption is not affected by the node density of sensor nodes because of the fixed transmission power. The variations for proposed EELA are also steady due to the strategy of the proposed game and the constant number of anchor nodes in this simulation setting.

From Fig. 4.4, I notice that the average energy consumption per sensor node in EELA (326 J) is about53 %lower than that in OLTC (693 J). This is thanks to our transmission power optimization strategy given the ‘one-hop’ and ‘two-hop’ nodes, which enables to reach the same number of anchor nodes as by OLTC, but with much lower energy. This mechanism significantly reduces the energy consumption of sensor nodes, and reduces the collisions of requests at the same time.

3) Average Energy Consumption Per Anchor Node: Fig. 4.5 illustrates the average energy consumption of anchor nodes in function of the number of sensor nodes.

I observe that the energy cost of proposed EELA and OLTC lies between that of EELA-Min and EELA-Max, with a higher consumption for EELA compared to OLTC.

3DUL-Max consumes roughly the same energy with EELA-Max while 3DUL-Min consumes slightly higher energy than EELA-Min. Namely, we can see that the average energy consumption per anchor node in EELA (about407 J) is nearly38 % higher than that in OLTC (about295 J). This is because anchor nodes in EELA need

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200 400 600 800 1,000 1,200

Number of Sensor Nodes

Avg.EnergyCostperAN(J)

EELA OLTC 3DUL-Min

3DUL-Max EELA-Min EELA-Max

Figure 4.5: Average energy consumption per Anchor Node (AN).

to broadcast twice in order to build their ‘two-hop’ anchor neighboring list. As for OLTC, anchor nodes do not need to consider about their ‘two-hop’ anchor neigh-boring nodes. As shown next, EELA slightly increases the energy consumption of anchor nodes in order to improve the performance of sensor nodes, which eventually improves the average energy consumption of all nodes. Note also that saving energy of underwater sensor nodes is a more crucial issue than that for anchor nodes, since anchor nodes are specifically deployed at the surface for enabling localization.

4) Average Energy Consumption for Any Node: Fig. 4.6 shows the average energy consumption over anchor and sensor nodes.

Overall, I observe that 3DUL-Max consumes the highest energy among all the schemes. The proposed scheme largely reduces the average energy cost per node, compared to OLTC, i.e., around48 %reduction. This shows that even if anchor nodes broadcast twice in the preprocessing phase, the proposed EELA still consumes much less energy in total, thanks to the energy-efficient power selection of sensor nodes.

This is because in the deployment of practical localization systems, the number of sensor nodes is much larger than that of anchor nodes.

Note also that as shown in [87], the main source of energy consumption in underwa-ter sensor nodes is transmission power, compared to any other functionality. Since the proposed and baseline schemes have similar algorithm complexities as shown in Section??, entailing similar power consumption for processing, I can conclude that

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200 400 600 800 1,000 1,200

Number of Sensor Nodes

Avg.EnergyCostperNode(J)

EELA OLTC 3DUL-Min

3DUL-Max EELA-Min EELA-Max

Figure 4.6: Average energy consumption per node.

the proposed EELA enables significant energy savings in a global manner.

5) Average Localization Delay and Error: Table 4.3 represents the Average Localization Delay (ALD) and Average Localization Error (ALE) of different schemes, where 3DMin and 3DMax are 3DUL-Min and 3DUL-Max, respectively. EMin and EMax are EELA-Min and EELA-Max, respectively.

I notice that the ALD of EELA is almost the same as that of OLTC. The ALD of EELA-Min is lower than that of EELA by nearly11 %on average. This is because in EELA-Min, the communication distance travelled by the acoustic signal is shorter than that in other schemes, since it uses the minimum transmission power. As for EELA-Max, the longer communication distance leads to higher delay since it uses maximum transmission power. In 3DUL-Min and 3DUL-Max, the ALD is larger due to the iterative localization design.

Next, for evaluating ALE, each sensor node requires three beacon locations and three distances from anchor nodes since the trilateration technique is considered. It is assumed that anchor nodes broadcast their precise coordinates, so the localization error is generated by the mobility of nodes and depends on the distance between anchor and sensor nodes. From Table 4.3, we can see that EELA performs slightly better than OLTC, while the lowest and highest ALE are achieved by EELA-Min and 3DUL-Max, respectively. Overall, the ALEs are at comparable and reasonable levels for all algorithms.

Metric EELA OLTC 3DMin 3DMax EMin EMax

ALD (s) 6.87 6.85 6.95 8.96 6.11 7.15

ALE (m) 3.18 3.24 3.29 3.97 3.17 3.30

Table 4.3: Average localization delay and error Metric 2 m s⁻¹ 3 m s⁻¹ 4 m s⁻¹ ALC (%) 96.24 96.16 96.26

AEN (J) 249.15 249.44 247.46

ALD (s) 6.90 6.89 6.89

Table 4.4: Average performance of EELA with different speed.